数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 1055-1066.doi: 10.1016/S0252-9602(15)30039-4

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A STABILIZED CRANK-NICOLSON MIXED FINITE VOLUME ELEMENT FORMULATION FOR THE NON-STATIONARY PARABOLIZED NAVIER-STOKES EQUATIONS

罗振东   

  1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
  • 收稿日期:2014-02-26 修回日期:2014-10-18 出版日期:2015-09-01 发布日期:2015-09-01
  • 作者简介:Zhendong LUO, E-mail: zhdluo@163.com,zhdluo@ncepu.edu.cn
  • 基金资助:

    Research of this work was mainly supported by National Science Foundation of China (11271127) and Science Research Project of Guizhou Province Education Department (QJHKYZ[2013]207).

A STABILIZED CRANK-NICOLSON MIXED FINITE VOLUME ELEMENT FORMULATION FOR THE NON-STATIONARY PARABOLIZED NAVIER-STOKES EQUATIONS

Zhendong LUO   

  1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
  • Received:2014-02-26 Revised:2014-10-18 Online:2015-09-01 Published:2015-09-01
  • Supported by:

    Research of this work was mainly supported by National Science Foundation of China (11271127) and Science Research Project of Guizhou Province Education Department (QJHKYZ[2013]207).

摘要:

A time semi-discrete Crank-Nicolson (CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element (SCNMFVE) formulation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided.

关键词: non-stationary parabolized Navier-Stokes equations, stabilized Crank-Nicolson mixed finite volume element formulation, error estimate

Abstract:

A time semi-discrete Crank-Nicolson (CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element (SCNMFVE) formulation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided.

Key words: non-stationary parabolized Navier-Stokes equations, stabilized Crank-Nicolson mixed finite volume element formulation, error estimate

中图分类号: 

  • 65N12